Diffusive limits of nonlinear hyperbolic systems with variable coefficients

Hironari Miyoshi, Masayoshi Tsutsumi

    Research output: Contribution to journalArticle

    Abstract

    We consider the initial-boundary value problem for a 2-speed system of first-order nonhomogeneous semilinear hyperbolic equations whose leading terms have a small positive parameter. Using energy estimates and a compactness lemma, we show that the diffusion limit of the sum of the solutions of the hyperbolic system, as the parameter tends to zero, verifies the nonlinear parabolic equation of the p-Laplacian type.

    Original languageEnglish
    Pages (from-to)1583-1599
    Number of pages17
    JournalContinuum Mechanics and Thermodynamics
    Volume28
    Issue number5
    DOIs
    Publication statusPublished - 2016 Sep 1

    Fingerprint

    hyperbolic systems
    Boundary value problems
    void ratio
    coefficients
    boundary value problems
    theorems
    estimates
    energy

    Keywords

    • Carleman’s equation
    • Diffusive limit
    • Initial boundary value problem
    • Nonlinear parabolic equation

    ASJC Scopus subject areas

    • Materials Science(all)
    • Mechanics of Materials
    • Physics and Astronomy(all)

    Cite this

    Diffusive limits of nonlinear hyperbolic systems with variable coefficients. / Miyoshi, Hironari; Tsutsumi, Masayoshi.

    In: Continuum Mechanics and Thermodynamics, Vol. 28, No. 5, 01.09.2016, p. 1583-1599.

    Research output: Contribution to journalArticle

    Miyoshi, Hironari ; Tsutsumi, Masayoshi. / Diffusive limits of nonlinear hyperbolic systems with variable coefficients. In: Continuum Mechanics and Thermodynamics. 2016 ; Vol. 28, No. 5. pp. 1583-1599.
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